L1-Based Adaptive Identification With Saturated Observations

• 成果类型: Article
• 署名作者: Zheng, Xin; Guo, Lei
• 署名单位: Chinese Academy of Sciences; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3547950
• 发表日期: 2025
• 页码: 5836-5847
• 关键词: Optimization; CONVERGENCE; vectors; Adaptive systems; accuracy; Stochastic processes; Prediction algorithms; Robustness; measurement; indexes; & ell; (1)-norm optimization; Adaptive identification; GLOBAL CONVERGENCE; saturated observations; Stochastic systems

摘要

It is well known that saturated output observations are prevalent in various practical systems and that the & ell;(1)-norm is more robust than the & ell;(2)-norm-based parameter estimation. Unfortunately, adaptive identification based on both saturated observations and the & ell;(1)-optimization turns out to be a challenging nonlinear problem, and has rarely been explored in the literature. Motivated by this and the need to fit with the & ell;(1)-based index of prediction accuracy in, e.g., judicial sentencing prediction problems, we propose a two-step weighted & ell;(1)-based adaptive identification algorithm. Under certain excitation conditions much weaker than the traditional persistent excitation condition, we will establish the global convergence of both the parameter estimators and the adaptive predictors. It is worth noting that our results do not rely on the widely used independent and identically distributed assumptions on the system signals, and thus, do not exclude applications to feedback control systems. We will demonstrate the advantages of our proposed new adaptive algorithm over the existing & ell;(2)-based ones, through both a numerical example and a real-data-based sentencing prediction problem.